A102128 a(1) = 1; a(n) = sum of previous terms which divide n.

1, 1, 2, 4, 2, 6, 2, 12, 2, 10, 2, 34, 2, 14, 2, 20, 2, 24, 2, 54, 2, 22, 2, 70, 2, 26, 2, 46, 2, 46, 2, 36, 2, 68, 2, 94, 2, 38, 2, 74, 2, 62, 2, 70, 2, 138, 2, 94, 2, 60, 2, 82, 2, 114, 2, 74, 2, 58, 2, 172, 2, 124, 2, 68, 2, 94, 2, 242, 2, 234, 2, 154, 2, 222, 2, 118, 2, 110, 2, 114, 2

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(1) = 1; a(n) = [x^n] Sum_{k=1..n-1} a(k)*x^a(k)/(1 - x^a(k)). - Ilya Gutkovskiy, Dec 11 2017

Example

Among the first 7 terms, the terms which divide 8 are 1, 1, 2, 4, 2 and 2.
So a(8) = 1 + 1 + 2 + 4 + 2 + 2 = 12.

Mathematica

Nest[Function[{a, n}, Append[a, Total@ Select[a, Mod[n, #] == 0 &]]] @@ {#, Length@ # + 1} &, {1}, 80] (* Michael De Vlieger, Nov 13 2018 *)

Prog

(PARI)
up_to = 20000;
A102128list(up_to) = { my(v=vector(up_to)); v[1] = 1; for(n=2, up_to, v[n] = sum(j=1, n-1, v[j]*!(n%v[j]))); (v); };
v102128 = A102128list(up_to);
A102128(n) = v102128[n]; \\ Antti Karttunen, Nov 10 2018

Crossrefs

Cf. A088167.

Sequence in context: A213372 A286601 A340071 * A181980 A230436 A105393

Adjacent sequences: A102125 A102126 A102127 * A102129 A102130 A102131

Keyword

nonn

Author

Leroy Quet, Feb 14 2005

Extensions

More terms from John W. Layman, Mar 16 2005

Status

approved